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QCD Sum Rules
In quantum chromodynamics, the confining and strong coupling nature of the theory means that conventional perturbative techniques often fail to apply. The QCD sum rules (or Shifman– Vainshtein–Zakharov sum rules) are a way of dealing with this. The idea is to work with gauge invariant operators and operator product expansions of them. The vacuum to vacuum correlation function for the product of two such operators can be reexpressed as :\left\langle 0 , T\left\ , 0 \right\rangle where we have inserted hadronic particle states on the right hand side. Overview Instead of a model-dependent treatment in terms of constituent quarks, hadrons are represented by their interpolating quark currents taken at large virtualities. The correlation function of these currents is introduced and treated in the framework of the operator product expansion (OPE), where the short and long-distance quark-gluon interactions are separated. The former are calculated using QCD perturbation theory, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Chromodynamics
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called ''color''. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years. QCD exhibits three salient properties: * Color confinement. Due to the force between two color charges remaining constant as they are separated, the energy grows until a quark–antiquark pair is spontaneously produced, turning the initial hadron into a pair of hadrons instead of isolating a color charge. Although ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Color Confinement
In quantum chromodynamics (QCD), color confinement, often simply called confinement, is the phenomenon that color-charged particles (such as quarks and gluons) cannot be isolated, and therefore cannot be directly observed in normal conditions below the Hagedorn temperature of approximately 2 terakelvin (corresponding to energies of approximately 130–140 MeV per particle). Quarks and gluons must clump together to form hadrons. The two main types of hadron are the mesons (one quark, one antiquark) and the baryons (three quarks). In addition, colorless glueballs formed only of gluons are also consistent with confinement, though difficult to identify experimentally. Quarks and gluons cannot be separated from their parent hadron without producing new hadrons. Origin There is not yet an analytic proof of color confinement in any non-abelian gauge theory. The phenomenon can be understood qualitatively by noting that the force-carrying gluons of QCD have color charge, unlike the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mikhail Shifman
Mikhail "Misha" Arkadyevich Shifman (russian: Михаи́л Арка́дьевич Ши́фман; born 4 April 1949) is a theoretical physicist (high energy physics), formerly at Institute for Theoretical and Experimental Physics, Moscow, Ida Cohen Fine Professor of Theoretical Physics, William I. Fine Theoretical Physics Institute, University of Minnesota. Scientific contributions Shifman is known for a number of basic contributions to quantum chromodynamics, the theory of strong interactions, and to understanding of supersymmetric gauge dynamics. The most important results due to M. Shifman are diverse and include (i) the discovery of the penguin mechanism in the flavor-changing weak decays (1974); (ii) introduction of the gluon condensate and development of the SVZ sum rules relating properties of the low-lying hadronic states to the vacuum condensates (1979); (iii) introduction of the invisible axion (1980) (iv) first exact results in supersymmetric Yang-Mills theories ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arkady Vainshtein
Arkady Vainshtein (russian: Аркáдий Иóсифович Вайнштéйн; born 24 February 1942) is a Russian and American Professor Emeritus of Theoretical physics who was awarded Pomeranchuk Prize (2005) and Sakurai Prize (1999) for theoretical physics. Biography Vainshtein was born on 24 February 1942 in Novokuznetsk, Russia. He got his Ph.D. from Budker Institute of Nuclear Physics in Novosibirsk, Russia and master's degree from Novosibirsk University where he became a Professor. He was the director of William I Fine Theoretical Physics Institute, University of Minnesota where he currently serves as the Gloria Becker Lubkin chair and also holds a position as Professor since 1990. In 1997 he became a fellow at the APS and two years later was awarded Sakurai Prize. In 2004 he started to work for Kavli Institute for Theoretical Physics in Santa Barbara, California, and a year later was awarded Pomeranchuk Prize from the Institute for Theoretical and Experimental Physics, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Valentin Ivanovich Zakharov
Valentin is a male given name meaning "strong, healthy, power, rule, terco". It comes from the Latin name ''Valentinus'', as in Saint Valentin. Commonly found in Spain, Romania, Bulgaria, France, Italy, Russia, Ukraine, Scandinavia, Latin America etc. Valentin is also used as a surname in Spanish and German speaking-countries. Given name First name * Valentin Abel (born 1991), German politician * Valentin Alexandru (born 1991), Romanian footballer * Valentin Blass (born 1995), German basketball player * Valentin Bondarenko (1937–1961), Soviet fighter pilot * Valentin de Boulogne (before 1591 – 1632), French painter * Valentin Brunel (born 1996), French DJ known as Kungs * Valentin "Val" Brunn (born 1994), German electronic music producer and DJ known as Virtual Riot * Valentin Bosioc (born 1983), Romanian bodybuilder * Valentín Castellanos (born 1998), Argentine footballer * Valentin Ceaușescu (born 1948), Romanian physicist * Valentin Chmerkovskiy (born 1986), Ukrainian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator Product Expansion
In quantum field theory, the operator product expansion (OPE) is used as an axiom to define the product of fields as a sum over the same fields. As an axiom, it offers a non-perturbative approach to quantum field theory. One example is the vertex operator algebra, which has been used to construct two-dimensional conformal field theories. Whether this result can be extended to QFT in general, thus resolving many of the difficulties of a perturbative approach, remains an open research question. In practical calculations, such as those needed for scattering amplitudes in various collider experiments, the operator product expansion is used in QCD sum rules to combine results from both perturbative and non-perturbative (condensate) calculations. 2D Euclidean quantum field theory In 2D Euclidean field theory, the operator product expansion is a Laurent series expansion associated to two operators. A Laurent series is a generalization of the Taylor series in that finitely many powers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Chromodynamics
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called ''color''. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years. QCD exhibits three salient properties: * Color confinement. Due to the force between two color charges remaining constant as they are separated, the energy grows until a quark–antiquark pair is spontaneously produced, turning the initial hadron into a pair of hadrons instead of isolating a color charge. Although ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice QCD
Lattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge theory formulated on a grid or lattice of points in space and time. When the size of the lattice is taken infinitely large and its sites infinitesimally close to each other, the continuum QCD is recovered. Analytic or perturbative solutions in low-energy QCD are hard or impossible to obtain due to the highly nonlinear nature of the strong force and the large coupling constant at low energies. This formulation of QCD in discrete rather than continuous spacetime naturally introduces a momentum cut-off at the order 1/''a'', where ''a'' is the lattice spacing, which regularizes the theory. As a result, lattice QCD is mathematically well-defined. Most importantly, lattice QCD provides a framework for investigation of non-perturbative phenomena such as confinement and quark–gluon plasma formation, which are intractable by means ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sum Rules (Quantum Field Theory)
In quantum field theory, a ''sum rule'' is a relation between a static quantity and an integral over a dynamical quantity. Therefore, they have a form such as: \int A(x) dx = B where A(x) is the dynamical quantity, for example a structure function characterizing a particle, and B is the static quantity, for example the mass or the charge of that particle. Quantum field theory sum rules should not be confused with sum rules in quantum chromodynamics or quantum mechanics. Properties Many sum rules exist. The validity of a particular sum rule can be sound if its derivation is based on solid assumptions, or on the contrary, some sum rules have been shown experimentally to be incorrect, due to unwarranted assumptions made in their derivation. The list of sum rules below illustrate this. Sum rules are usually obtained by combining a dispersion relation with the optical theorem, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sum Rule In Quantum Mechanics
In quantum mechanics, a sum rule is a formula for transitions between energy levels, in which the sum of the transition strengths is expressed in a simple form. Sum rules are used to describe the properties of many physical systems, including solids, atoms, atomic nuclei, and nuclear constituents such as protons and neutrons. The sum rules are derived from general principles, and are useful in situations where the behavior of individual energy levels is too complex to be described by a precise quantum-mechanical theory. In general, sum rules are derived by using Heisenberg's quantum-mechanical algebra to construct operator equalities, which are then applied to the particles or energy levels of a system. Derivation of sum rules Assume that the Hamiltonian \hat has a complete set of eigenfunctions , n\rangle with eigenvalues E_n: : \hat , n\rangle = E_n , n\rangle. For the Hermitian operator In mathematics, a self-adjoint operator on an infinite-dimensional complex vector space ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
